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MathematicsClass 8Pythagoras Theorem

Pythagoras Theorem | Class 8 Mathematics Notes

By ConceptScroll Team · Published on 17 July 2026 · 3 min read

Pythagoras Theorem – this guide gives you a concise, exam-ready overview of Pythagoras Theorem from Class 8 Mathematics, written by ConceptScroll editors and reviewed against the latest NCERT textbook.

Applications of Pythagoras Theorem

The Pythagoras Theorem has many practical applications in daily life and various professions. It is used to determine distances that are not directly measurable, such as the length of a ladder needed to reach a certain height, the shortest distance between two points, or the diagonal of rectangular objects. In construction, it helps in ensuring structures are built with right angles. In navigation, it assists in calculating shortest paths. For example, if a ladder leans against a wall, the height it reaches can be found using the theorem if the distance from the wall and the length of the ladder are known. Similarly, the diagonal of a rectangular field or a TV screen can be calculated. These applications demonstrate the theorem's importance beyond theoretical mathematics, showing its relevance in real-world problem-solving.

📊 Diagram: Diagrams include a ladder leaning against a wall forming a right triangle, and a rectangle with its diagonal marked, illustrating the use of the theorem to find unknown lengths.

🧪 Activity: No specific activity; examples illustrate applications.

🔗 Connection: Leads to exercises and problems for practice in the next section.

Frequently asked questions

1. Find the diagonal of a square with sidelength 5 cm.

The diagonal d of a square with side length a is given by the Pythagoras theorem: d = √(a² + a²) = √(2a²) = a√2. Here, a = 5 cm, so d = 5√2 cm ≈ 7.07 cm.

2. Find the missing sidelengths in the following right triangles: [The textbook shows several right triangles with some sides missing.]

Use the Pythagoras theorem a² + b² = c² where c is the hypotenuse.

For each triangle:

  • Triangle with sides 4, 7, and missing side 10: Check if 4² + 7² = 10²? 16 + 49 = 65, 10²=100, no. So missing side must be calculated accordingly.
  • Triangle with sides 9, 10, and missing side 41: Since 41 is large, likely hypotenuse.
  • Triangle with sides 40, 45, and missing side 27: Calculate missing side using Pythagoras theorem.
  • Triangle with sides 10, 150, and missing side 3: Check which is hypotenuse
3. Find the sidelength of a rhombus whose diagonals are of length 24 units and 70 units.

The diagonals of a rhombus bisect each other at right angles. Each side of the rhombus is the hypotenuse of a right triangle with legs half the diagonals.

Half diagonals: 24/2 = 12 units, 70/2 = 35 units.

Side length = √(12² + 35²) = √(144 + 1225) = √1369 = 37 units.

4. Is the hypotenuse the longest side of a right triangle? Justify your answer.

Yes, the hypotenuse is always the longest side of a right triangle. This is because, according to the Pythagoras theorem, the square of the hypotenuse equals the sum of the squares of the other two sides, so it must be longer than either of them.

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